carnot's theory of the motive power of heat. 557 



The values of this integral may be practically obtained, in the most con- 

 venient manner, by first determining, from observation, the mean values of fi 

 for the successive degrees of the thermometric scale, and then adding the values 

 for all the degrees within the limits of the extreme temperatures S and T.* 



32. The complete theoretical investigation of the motive power of heat is thus 

 reduced to the experimental determination of the coefficient ^ ; and may be con- 

 sidered as perfect, when, by any series of experimental researches whatever, we 

 can find a value of ^ for every temperature within practical limits. The special 

 character of the experimental researches, Avhether with reference to gases, or with 

 reference to vapours, necessary and sufficient for this object, is defined and re- 

 stricted in the most precise manner, by the expressions (G) for jj., given above. 



33. The object of Regnault's great work, referred to in the title of this 

 paper, is the experimental determination of the various physical elements of the 

 steam-engine ; and when it is complete, it will furnish all the duta necessary for 

 the calculation of /*. The valuable researches already published in a first part of 

 that work, make known the latent heat of a given weight, and the pressure, of 

 saturated steam for all temperatures between 0" and 230' cent, of the air-thermo- 

 meter. Besides these data, however, the density of saturated vapour must be 

 known, in order that A-, the latent heat of a unit of volume, may be calculated from 

 Regnault's determination of the latent heat of a given weight.f Between the 

 limits of 0° and 100°, it is probable, from various experiments which have been 

 made, that the density of vapour follows very closely the simple laws which are 

 so accurately verified by the ordinary gases \\ and thus it may be calculated from 

 Regnault's table giving the pressure at any temperature within those limits. 

 Nothing as yet is known with accuracy as to the density of saturated steam between 

 100° and 230°, and we must be contented at present to estimate it by calculation 

 from Regnault's table of pressures ; although, when accurate experimental re- 

 searches on the subject shall have been made, considerable deviations from the 

 laws of Boyle and Dalton, on which this calculation is founded, may be disco- 

 vered. 



* The results of these investigations are exhibited in Tables I. and II. below. 



t It is, comparatively speaking, of Little consequence to know accurately the value of ir, for the 

 factor (1 — ff) of the expression for /i, since it is so small (being less than y J^, for all temperatures 

 between 0° and 100°) that, unless all the data are known with more accuracy than we can count 



upon at present, we might neglect it altogether, and take — — - simply, as the expression for /i, with- 



dt 

 IT 



out committing any error of important magnitude. , 



t This is well established, within the ordinary atmospheric limits, in Regnault's Etudes Me- 

 teorologiques, in the Annales de Chimie, vol. xv., 1846. 



VOL. XVI. PAET V. 7 E 



